uf3.regression.regularize.get_penalty_matrix_2D

get_penalty_matrix_2D(L: int, M: int, ridge: float = 0.0, curvature: float = 1.0) → numpy.ndarray

Generates additive regularization matrix for linear regression

using curvature penalty and/or L2 (ridge) penalty. Curvature penalty here applies to coefficients that are spatially related in two dimensions that may not be adjacent after flattening for linear least-squares.

Parameters

• L (int) – length of coefficient matrix before flattening.

• M (int) – width of coefficient matrix before flattening.

• ridge (float) – L2 (ridge) regularization strength.

• curvature (float) – Local curvature regularization strength.

Returns

square penalty matrix for linear

least-squares of shape (L*M , L*M).

Return type

matrix_2d (numpy.ndarray)